On the collective excitation spectrum of the electron Wigner crystal on the surface of liquid helium

A self-consistent equation set is proposed which describes the effect of deformation of the surface of liquid helium (occurring at the Wigner cristallization on surface electrons) on the collective excitation spectrum of two-dimensional crystal. A solution of the equation set in the harmonic approximation reveals the existance in the longitudinal and transverse oscillation spectrum of two-dimensional crystal of a threshold ωsub(o) frequency of deformation origin. A study is made of the dependence of ωsub(o) on the parameters of the problem, such as the intensity of the pressing electric field E surface electron density nsub(s) and temperature. The problem solution provides the possibility to find a number of ωsub(o) quantitative characteristics in electron spectrum. The Wigner crystal oscillation dispersion becomes small not only in the region of electron low surface density but also in the region higher than boundary dispersion. For the case of small dispersion the harmonic approach solution of the Wigner crystal spectrum problem on helium selfmatched deformed surface has both quantitative and qualitative meanings